Download Chapter 6 Test, Form 3

6
DATE
PERIOD
Chapter 6 Test, Form 3
Graph each system of equations. Determine whether the
system has no solution, one solution, or infinitely many
solutions. If the system has one solution, name it.
1
1. −
y=x
3
y+x+4=0
SCORE
1.
1
y=x
3
3x - 4y = 8
x
O
2. x + 3y = 3
y+x+4=0
3y = -x + 9
Use substitution to solve each system of equations. If the
system does not have exactly one solution, state whether
it has no solution or infinitely many solutions.
3. y = 2x - 7
y
one solution; (-1, -3)
AM-60C-827731-A
y 3y = -x + 9
4. 4y - 3x = 5
x
3
−
x=y-4
O
4
x + 3y = 3
5. x - 2y = -3
y = 3x - 1
6. y = -x + 3
x + y = -1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Use elimination to solve each system of equations.
7. 6x - 7y = 21
3x + 7y = 6
2
y = -8
9. 2x + −
3
1
1
−
x-−
y=1
2
3
8. 0.2x + 0.5y = 0.7
-0.2x - 0.6y = -1.4
1
2
10. −
x+−
y = -10
2
5
25x + 10y = 2415
1
- 2x
12. 7y = 2−
2
5x = 3y - 4
13. Three times one number added to five times a second
number is 68. Three times the second number minus four
times the first number is 6. What are the two numbers?
14. The difference of two numbers is 5. Five times the lesser
number minus the greater number is 9. What are the two
numbers?
15. A trail mix that costs $2.45 per pound is mixed with a
trail mix that costs $2.30 per pound. How much of each
type of trail mix must be used to have 30 pounds of a
trail mix that costs $2.35 per pound?
Chapter 6
5.
(1, 2)
6.
no solution
7.
(3, - −37 )
3x + 6y = -6
Determine the best method to solve each system of
equations. Then solve the system.
11. x + y = 147
no solution
AM-61C-827731-A
(4, 1)
3.
no solution
4.
2.
61
8.
(-14, 7)
9.
(-2, -6)
(-32, 15)
10.
11. substitution; (63, 84)
elimination (×);
12.
13.
14.
(- −12 , −12 )
6, 10
1
1
3−
, 8−
2
2
10 lb of $2.45 mix;
15. 20 lb of $2.30 mix
Glencoe Algebra 1
Assessment
NAME
NAME
DATE
6
Chapter 6 Test, Form 3
PERIOD
(continued)
16. A boat travels 60 miles downstream in the same time it
takes to go 36 miles upstream. The speed of the boat in
still water is 15 mph greater than the speed of the current.
Find the speed of the current.
16.
5 mph
For Questions 17 and 18, solve the system of inequalities
by graphing.
1
x+2
17. y < - −
17.
4
y
y≤x-1
O
18. -2x - y > 1
18.
1
−
x-y≤1
x
y
C06-12A-890500-A
2
O
x
Bonus Find the area of the polygon formed by the system of
equations y = 0, y = 2x + 4 and -3y - 4x = -12.
Chapter 6
62
B:
10 square units
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
19. Mr. Nordmann gets a commission of $2.50 on each pair of
women’s shoes he sells, and a commission of $3 on each pair
C06-13A-890500-A
of men’s shoes he sells. To meet his sales targets, he must sell
x = women’s shoes
at least 10 pairs of women’s shoes and at least 5 pairs of
sold; y = men’s shoes
men’s shoes. He also wants to make at least $60 a week in
sold; x ≥ 10, y ≥ 5,
commissions. Define the variables, write a system of
2.5x + 3y ≥ 60; sample
inequalities to represent this situation, and name one possible
answer: (15, 10)
solution.
19.